The invention relates to the field of Cherenkov radiation, and in particular to using photonic crystals as a medium to exhibit anomalous Cherenkov radiation.
Cherenkov radiation (CR) is the coherent electromagnetic response of a medium driven by the swift passage of a charged particle. It is thus an effect strongly dependent on the medium dispersion. In a uniform, isotropic medium with frequency-independent permittivity ∈ and permeability xcexc, the condition for CR is well-known, where the velocity of the particle v must exceed the phase velocity of the medium "ugr"ph=c/√{square root over (∈xcexc)}. For a dispersive medium, such as a nonmagnetic material with a Lorentz-form dielectric response ∈(xcfx89), "ugr"ph(xcfx89)=c/√{square root over (∈(xcfx89))}, is a function of frequency xcfx89. Because ∈(xcfx89) can reach arbitrarily high values near a resonance, it was long recognized that CR in a dispersive medium can happen for small charge velocities, e.g., "ugr" less than "ugr"ph(0). The sub-threshold CR in a material near its phonon-polariton resonance was disclosed in Cherenkov Radiation at Speeds Below the Light Threshold: Phonon-Assisted Phase Matching, by T. E. Stevens, J. K. Wahlstrand, J. Kuhl, and R. Merlin, SCIENCE, vol. 291, No. 5504 (26 Jan. 2001).
On the other hand, it was conjectured that there could exist another class of materials which have both ∈ and xcexc being negative, henceforth referred to as xe2x80x9cnegative index materials.xe2x80x9d The properties of such materials were disclosed in The Electrodynamics of Substances with Simultaneously Negative Values of ∈ and xcexc, by V. G. Veselago, SOVIET PHYSICS USPEKHI, vol. 10, No. 4 (January-February 1968). It was suggested that a negative index material would reverse many of the well-known laws of optics. In particular, CR effect is predicted to be reversed, i.e., a fast-moving charge in a negative index medium should radiate in the direction opposite to that of its velocity.
A further possibility exists when the charged particle travels near a periodic structure, where simple Bragg scattering can give rise to radiation without any velocity threshold. This phenomenon (the Smith-Purcell effect) was disclosed in Visible Light from Localized Surface Charges Moving across a Grating, by S. J. Smith and P. M. Purcell, PHYSICAL REVIEW, vol. 92, No. 4 (15 Nov. 1953). The radiation due to traveling charged particles has since been studied in one-dimensionally periodic multilayer stacks in Cerenkov Radiation in Inhomogeneous Periodic Media, by K. F. Casey, C. Yeh, and Z. A. Kaprielian, PHYSICAL REVIEW, vol. 140, No. 3B (8 Nov. 1965), and near the surface of dielectric structures in Interactions of Radiation and Fast Electrons with Clusters of Dielectrics: A Multiple Scattering Approach, by F. J. Garcia de Abajo, PHYSICAL REVIEW LETTERS, vol. 82, No. 13 (29 Mar. 1999).
According to one aspect of the invention, there is provided a system for exhibiting Cherenkov radiation. The system includes a beam of traveling charged particles. A photonic crystal structure receives the beam of charged particles. The charged particles move in the photonic crystal structure so that CR is produced at all velocities without requiring resonances in the effective material constants of said photonic crystal structure.
According to another aspect of the invention, there is provided a method of exhibiting Cherenkov radiation. The method includes providing a beam of traveling charged particles. Also, the method includes providing a photonic crystal structure that receives the beam of charged particles. The charged particles move in the photonic crystal structure so that Cherenkov radiation is produced at all velocities without requiring resonances in the effective material constants of said photonic crystal structure.